Page - 48 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

4. Measurements Table 4.1.: Recorded channels Channel description Symbol(s) Source video data - camera vehicle speed vvx vehicle data bus vehicle yaw rate vωz wheel speed clfvx,crfvx,crrvx,clfvx steering wheel angle δSW position of object sx,sy RADAR sensor relative speed of object svx,svy probability of existence of object pex length, width of object sl,sw position of target vx,vy,vz ADMA longitudinal, lateral, vertical speed vvx,vvy,vvz longitudinal, lateral, vertical acceleration vax,vay,vaz rotational speeds around axis vx,vy,vz vωx,vωy,vωz relative heading of target to ego vψ position of the ego vehicle 0x,0y,0z side slip angle at CG β calculated, eq. (4.13) withx= [ β vωz ]T . Fo¨llingershowedin[Fo¨l08]thatasingleoutputsystemisobservable if the observability matrix reading QB=      cT cT A ... cT An−1      (4.3) for a system with the state vector consisting ofn components is non-singular, meaning detQB 6= 0. (4.4) For a more compact notation, the system matrix A of the linear STM of eq. (B.8) is denoted as A= [ a11 a12 a21 a22 ] . (4.5) This leads to a observability matrix of QB= [ 0 1 a21 a22 ] . (4.6) The requirement described in eq. (4.4) leads to rcy lr 6= fcy lf, which is fulfilled for a vehicle in general. 48